Finite Group Databasebeta

← C11×#35008 #14612201

Subgroups — C11×#35008 #14612201

Order 2816.

2284 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#539C212yesmaximal, complemented
2C11×#2860C211yesmaximal, characteristic, complemented
3C11×#2859C211yesmaximal, characteristic, complemented
4C11×#2857C211yesmaximal, characteristic, complemented
5C11×#2854C211yesmaximal, characteristic, complemented
6C11×#2664C212yesmaximal, complemented
7C11×#2663C212yesmaximal, complemented
8C11×#2556C212yesmaximal, complemented
9C11×#2553C212yesmaximal, complemented
10C11×#2506C211yesmaximal, characteristic, complemented
11C11×#2501C211yesmaximal, characteristic, complemented
12C11×#2496C211yesmaximal, characteristic, complemented
13C11×#2488C212yesmaximal, complemented
14C11×#2486C211yesmaximal, characteristic, complemented
15C11×#2452C211yesmaximal, characteristic, complemented
16C11×#2440C211yesmaximal, characteristic, complemented
17C11×#2425C212yesmaximal, complemented
18C11×#2422C211yesmaximal, characteristic, complemented
19C11×#2416C211yesmaximal, characteristic
20C11×#2322C212yesmaximal, complemented
21C4×C11×#121C211yesmaximal, characteristic, complemented
22C2×C11×#389C211yesmaximal, characteristic, complemented
23C42×D4×C11C211yesmaximal, characteristic, complemented
24C11×#539—216no—
25C2×C11×C4⋊Q8C2211yescharacteristic
26C2×C11×#126C2212yes—
27C2×C11×#126C2212yes—
28C2×C11×#125C2212yes—
29C2×C11×#125C2212yes—
30C2×C11×#123C2212yes—
31C2×C11×#123C2212yes—
32C2×C11×#123C2212yes—
33C2×C11×#123C2212yes—
34C2×C11×#123C2212yes—
35C2×C11×C22⋊Q8C2212yes—
36C2×C11×C22⋊Q8C2212yes—
37C2×C11×C22⋊Q8C2212yes—
38C2×C11×#121C2212yes—
39C2×C11×#121C2211yescharacteristic
40C2×C11×#121C2211yescharacteristic
41C2×C4×D4×C11C2211yescharacteristic
42C2×C4×D4×C11C2211yescharacteristic
43C2×C4×D4×C11C2212yes—
44C2×C4×D4×C11C2211yescharacteristic
45C2×C4×D4×C11C2211yescharacteristic
46C22×C11×C4⋊C4C2212yes—
47C22×C11×C4⋊C4C2211yescharacteristic
48C22×C11×C4⋊C4C2211yescharacteristic
49C22×C42×C11C2211yescharacteristic
50C22×C42×C11C2211yescharacteristic
51C11×#400C2212yes—
52C11×#400C2212yes—
53C11×#399C2212yes—
54C11×#399C2212yes—
55C11×#398C2212yes—
56C11×#398C2212yes—
57C11×#398C2212yes—
58C11×#397C2212yes—
59C11×#397C2212yes—
60C11×#397C2212yes—
61C11×#396C2212yes—
62C11×#396C2212yes—
63C11×#395C2212yes—
64C11×#394C2212yes—
65C11×#394C2212yes—
66C11×#393C2212yes—
67C11×#391C2212yes—
68C11×#390C2211yescharacteristic
69C11×#390C2211yescharacteristic
70C11×#390C2211yescharacteristic
71C11×#390C2211yescharacteristic
72C11×#389C2212yes—
73C11×#389C2212yes—
74C11×#389C2212yes—
75C11×#389C2211yescharacteristic
76C11×#389C2211yescharacteristic
77C11×#389C2212yes—
78C11×#389C2211yescharacteristic
79C11×#389C2211yescharacteristic
80C11×#389C2211yescharacteristic
81C11×#389C2211yescharacteristic
82C11×#389C2211yescharacteristic
83C11×#389C2212yes—
84C11×#389C2211yescharacteristic
85C11×#389C2211yescharacteristic
86C11×#389C2211yescharacteristic
87C11×#388C2212yes—
88C11×#388C2212yes—
89C11×#388C2212yes—
90C11×#388C2212yes—
91C11×#388C2212yes—
92C11×#388C2212yes—
93C11×#387C2212yes—
94C11×#387C2212yes—
95C11×#386C2212yes—
96C11×#386C2212yes—
97C11×#386C2212yes—
98C11×#385C2212yes—
99C11×#385C2212yes—
100C11×#385C2212yes—
101C11×#384C2211yescharacteristic
102C11×#384C2211yescharacteristic
103C11×#384C2211yescharacteristic
104C11×#382C2212yes—
105C11×#381C2212yes—
106C11×#380C2211yescharacteristic
107C11×#380C2211yescharacteristic
108C11×#380C2212yes—
109C11×#380C2211yescharacteristic
110C11×#380C2211yescharacteristic
111C4×C11×C4⋊C4C2211yescharacteristic
112C4×C11×C4⋊C4C2211yescharacteristic
113C4×C11×C4⋊C4C2211yescharacteristic
114C4×C11×C4⋊C4C2211yescharacteristic
115C4×C11×C22⋊C4C2211yescharacteristic
116C4×C11×C22⋊C4C2211yescharacteristic
117C4×C11×C22⋊C4C2211yescharacteristic
118C4×C11×C22⋊C4C2211yescharacteristic
119C4×C11×C22⋊C4C2211yescharacteristic
120C4×C11×C22⋊C4C2211yescharacteristic
121C4×C11×C22⋊C4C2212yes—
122C2×C11×#95C2212yes—
123C43×C11C2211yescharacteristic
124C22×Q8×C11C2312yes—
125C22×D4×C11C2312yes—
126C22×D4×C11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C22×D4×C11C2312yes—
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2312yes—
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2311yescharacteristic
133C23×C4×C11C2311yescharacteristic
134C23×C4×C11C2312yes—
135C23×C4×C11C2312yes—
136C23×C4×C11C2311yescharacteristic
137C23×C4×C11C2311yescharacteristic
138C11×C4⋊Q8—42no—
139C11×#126—28no—
140C11×#126—28no—
141C11×#125—28no—
142C11×#125—28no—
143C11×#123—28no—
144C11×#123—28no—
145C11×#123—28no—
146C11×#123—28no—
147C11×#123—28no—
148C11×C22⋊Q8—28no—
149C11×C22⋊Q8—28no—
150C11×C22⋊Q8—28no—
151C11×#121—28no—
152C11×#121—24no—
153C11×#121—42no—
154C4×D4×C11—28no—
155C4×D4×C11—24no—
156C4×D4×C11—24no—
157C4×D4×C11—42no—
158C4×D4×C11D418yescomplemented
159C2×C11×C4⋊C4—28no—
160C2×C11×C4⋊C4—24no—
161C2×C11×C4⋊C4—42no—
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C4⋊C4C2311yescharacteristic
166C2×C11×C4⋊C4C2312yes—
167C2×C11×C4⋊C4C2312yes—
168C2×C11×C4⋊C4C2312yes—
169C2×C11×C4⋊C4C2312yes—
170C2×C11×C4⋊C4C2312yes—
171C2×C11×C4⋊C4C2311yescharacteristic
172C2×C11×C4⋊C4C2311yescharacteristic
173C2×C11×C4⋊C4C2311yescharacteristic
174C2×C11×C4⋊C4C2312yes—
175C2×C11×C4⋊C4C2311yescharacteristic
176C2×C11×C4⋊C4C2311yescharacteristic
177C2×C11×C4⋊C4C2312yes—
178C2×C11×C4⋊C4C2312yes—
179C2×C11×C4⋊C4C2312yes—
180C2×C11×C4⋊C4C2312yes—
181C2×C11×C4⋊C4C2312yes—
182C2×C11×C4⋊C4C2312yes—
183C2×C11×C4⋊C4C2312yes—
184C2×C11×C4⋊C4C2312yes—
185C2×C11×C4⋊C4C2312yes—
186C2×C11×C4⋊C4C2312yes—
187C2×C11×C4⋊C4C2312yes—
188C2×C11×C4⋊C4C2312yes—
189C2×C11×C4⋊C4C2312yes—
190C2×C11×C4⋊C4C2311yescharacteristic
191C2×C11×C22⋊C4C2311yescharacteristic
192C2×C11×C22⋊C4C2311yescharacteristic
193C2×C11×C22⋊C4C2311yescharacteristic
194C2×C11×C22⋊C4C2312yes—
195C2×C11×C22⋊C4C2312yes—
196C2×C11×C22⋊C4C2312yes—
197C2×C11×C22⋊C4C2312yes—
198C2×C11×C22⋊C4C2312yes—
199C2×C11×C22⋊C4C2312yes—
200C2×C11×C22⋊C4C2312yes—
201C2×C11×C22⋊C4C2312yes—
202C2×C11×C22⋊C4C2312yes—
203C2×C11×C22⋊C4C2312yes—
204C2×C11×C22⋊C4C2312yes—
205C2×C11×C22⋊C4C2312yes—
206C2×C11×C22⋊C4C2312yes—
207C2×C11×C22⋊C4C2312yes—
208C2×C11×C22⋊C4C2312yes—
209C2×C11×C22⋊C4C2311yescharacteristic
210C2×C11×C22⋊C4C2311yescharacteristic
211C2×C11×C22⋊C4C2311yescharacteristic
212C2×C42×C11—42no—
213C2×C42×C11—42no—
214C2×C42×C11C2311yescharacteristic
215C2×C42×C11C2311yescharacteristic
216C2×C42×C11C2311yescharacteristic
217C2×C42×C11C2311yescharacteristic
218C2×C42×C11C2311yescharacteristic
219C2×C42×C11C2311yescharacteristic
220C2×C42×C11C2311yescharacteristic
221C2×C42×C11C2312yes—
222C2×C42×C11C2311yescharacteristic
223C2×C42×C11C2311yescharacteristic
224C2×C42×C11C2311yescharacteristic
225C2×C42×C11C2311yescharacteristic
226C2×C42×C11C2311yescharacteristic
227C2×C42×C11C2311yescharacteristic
228C11×#95C2312yes—
229C11×#95C2312yes—
230C11×#95C2312yes—
231C11×#95C2312yes—
232C11×#95C2311yescharacteristic
233C11×#95C2311yescharacteristic
234C11×#95C2311yescharacteristic
235C11×#95C2311yescharacteristic
236C11×#95C2311yescharacteristic
237C11×#95C2311yescharacteristic
238C11×#95C2312yes—
239C11×#95C2312yes—
240C11×#95C2312yes—
241C11×#95C2312yes—
242C11×#95C2312yes—
243C11×#95C2312yes—
244C11×#95C2312yes—
245C11×#95C2312yes—
246C11×#95C2312yes—
247C11×#95C2312yes—
248C11×#95C2312yes—
249#35008C1111yesmaximal, characteristic, direct product factor, Sylow
250C24×C11C2412yes—
251C24×C11C2411yescharacteristic
252C24×C11C2411yescharacteristic
253C2×Q8×C11—24no—
254C2×Q8×C11—42no—
255C2×Q8×C11—42no—
256C2×D4×C11—22no—
257C2×D4×C11—22no—
258C2×D4×C11—24no—
259C2×D4×C11—24no—
260C2×D4×C11—24no—
261C2×D4×C11—24no—
262C2×D4×C11—22no—
263C2×D4×C11—22no—
264C2×D4×C11—22no—
265C2×D4×C11—42no—
266C2×D4×C11—42no—
267C2×D4×C11C2×D414yes—
268C22×C4×C11—22no—
269C22×C4×C11—22no—
270C22×C4×C11—24no—
271C22×C4×C11—24no—
272C22×C4×C11—22no—
273C22×C4×C11—24no—
274C22×C4×C11—24no—
275C22×C4×C11—22no—
276C22×C4×C11—22no—
277C22×C4×C11—22no—
278C22×C4×C11—22no—
279C22×C4×C11—22no—
280C22×C4×C11—22no—
281C22×C4×C11—24no—
282C22×C4×C11—41no—
283C22×C4×C11—41no—
284C22×C4×C11—41no—
285C22×C4×C11—41no—
286C22×C4×C11—41no—
287C22×C4×C11—41no—
288C22×C4×C11—42no—
289C22×C4×C11—42no—
290C22×C4×C11—42no—
291C22×C4×C11—42no—
292C22×C4×C11C2×D414yes—
293C22×C4×C11C2×D414yes—
294C22×C4×C11#4114yes—
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2412yes—
299C22×C4×C11C2412yes—
300C22×C4×C11C2412yes—
301C22×C4×C11C2412yes—
302C22×C4×C11C2412yes—
303C22×C4×C11C2412yes—
304C22×C4×C11C2412yes—
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2411yescharacteristic
307C22×C4×C11C2411yescharacteristic
308C22×C4×C11C2411yescharacteristic
309C22×C4×C11C2411yescharacteristic
310C22×C4×C11C2411yescharacteristic
311C22×C4×C11C2411yescharacteristic
312C22×C4×C11C2411yescharacteristic
313C22×C4×C11C2411yescharacteristic
314C22×C4×C11C2411yescharacteristic
315C11×C4⋊C4—24no—
316C11×C4⋊C4—24no—
317C11×C4⋊C4—24no—
318C11×C4⋊C4—24no—
319C11×C4⋊C4—24no—
320C11×C4⋊C4—24no—
321C11×C4⋊C4—24no—
322C11×C4⋊C4—24no—
323C11×C4⋊C4—24no—
324C11×C4⋊C4—24no—
325C11×C4⋊C4—24no—
326C11×C4⋊C4—24no—
327C11×C4⋊C4—24no—
328C11×C4⋊C4—24no—
329C11×C4⋊C4—22no—
330C11×C4⋊C4—22no—
331C11×C4⋊C4—22no—
332C11×C4⋊C4—22no—
333C11×C4⋊C4—22no—
334C11×C4⋊C4—24no—
335C11×C4⋊C4—24no—
336C11×C4⋊C4—22no—
337C11×C4⋊C4—22no—
338C11×C4⋊C4—22no—
339C11×C4⋊C4—22no—
340C11×C4⋊C4—42no—
341C11×C4⋊C4—42no—
342C11×C4⋊C4—42no—
343C11×C4⋊C4C2×D414yes—
344C11×C22⋊C4—24no—
345C11×C22⋊C4—24no—
346C11×C22⋊C4—24no—
347C11×C22⋊C4—24no—
348C11×C22⋊C4—22no—
349C11×C22⋊C4—24no—
350C11×C22⋊C4—24no—
351C11×C22⋊C4—24no—
352C11×C22⋊C4—24no—
353C11×C22⋊C4—22no—
354C11×C22⋊C4—22no—
355C11×C22⋊C4—24no—
356C11×C22⋊C4—24no—
357C11×C22⋊C4—24no—
358C11×C22⋊C4—24no—
359C11×C22⋊C4—42no—
360C11×C22⋊C4—42no—
361C11×C22⋊C4—42no—
362C11×C22⋊C4C2×D414yes—
363C11×C22⋊C4C2×D414yes—
364C11×C22⋊C4#4114yes—
365C42×C11—24no—
366C42×C11—22no—
367C42×C11—22no—
368C42×C11—22no—
369C42×C11—22no—
370C42×C11—22no—
371C42×C11—22no—
372C42×C11—22no—
373C42×C11—41no—
374C42×C11—41no—
375C42×C11—41no—
376C42×C11—41no—
377C42×C11—41no—
378C42×C11C2×D414yes—
379C2×#539C2×C1112yescomplemented
380#2860C2×C1111yescharacteristic, complemented
381#2859C2×C1111yescharacteristic, complemented
382#2857C2×C1111yescharacteristic, complemented
383#2854C2×C1111yescharacteristic, complemented
384#2664C2×C1112yescomplemented
385#2663C2×C1112yescomplemented
386#2556C2×C1112yescomplemented
387#2553C2×C1112yescomplemented
388#2506C2×C1111yescharacteristic, complemented
389#2501C2×C1111yescharacteristic, complemented
390#2496C2×C1111yescharacteristic, complemented
391#2488C2×C1112yescomplemented
392#2486C2×C1111yescharacteristic, complemented
393#2452C2×C1111yescharacteristic, complemented
394#2440C2×C1111yescharacteristic, complemented
395#2425C2×C1112yescomplemented
396#2422C2×C1111yescharacteristic, complemented
397#2416C2×C1111yescharacteristic
398#2322C2×C1112yescomplemented
399C4×#121C2×C1111yescharacteristic, complemented
400C2×#389C2×C1111yescharacteristic, complemented
401C42×D4C2×C1111yescharacteristic, complemented
402C23×C11—21no—
403C23×C11—21no—
404C23×C11—21no—
405C23×C11—21no—
406C23×C11—21no—
407C23×C11—21no—
408C23×C11—21no—
409C23×C11—21no—
410C23×C11—21no—
411C23×C11—21no—
412C23×C11—22no—
413C23×C11—22no—
414C23×C11—22no—
415C23×C11—22no—
416C23×C11—22no—
417C23×C11—22no—
418C23×C11—22no—
419C23×C11C22×D412yes—
420C23×C11C22×D412yes—
421C23×C11C2×#4112yes—
422C23×C11C2×#4112yes—
423C23×C11C2511yescharacteristic
424Q8×C11—84no—
425D4×C11—28no—
426D4×C11—48no—
427D4×C11—44no—
428D4×C11—84no—
429C2×C4×C11—21no—
430C2×C4×C11—21no—
431C2×C4×C11—21no—
432C2×C4×C11—21no—
433C2×C4×C11—21no—
434C2×C4×C11—21no—
435C2×C4×C11—21no—
436C2×C4×C11—21no—
437C2×C4×C11—21no—
438C2×C4×C11—21no—
439C2×C4×C11—21no—
440C2×C4×C11—21no—
441C2×C4×C11—21no—
442C2×C4×C11—21no—
443C2×C4×C11—21no—
444C2×C4×C11—21no—
445C2×C4×C11—21no—
446C2×C4×C11—21no—
447C2×C4×C11—28no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—21no—
456C2×C4×C11—22no—
457C2×C4×C11—22no—
458C2×C4×C11—21no—
459C2×C4×C11—21no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—22no—
463C2×C4×C11—22no—
464C2×C4×C11—21no—
465C2×C4×C11—21no—
466C2×C4×C11—22no—
467C2×C4×C11—22no—
468C2×C4×C11—22no—
469C2×C4×C11—21no—
470C2×C4×C11—22no—
471C2×C4×C11—22no—
472C2×C4×C11—21no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—22no—
476C2×C4×C11—22no—
477C2×C4×C11—22no—
478C2×C4×C11—44no—
479C2×C4×C11—44no—
480C2×C4×C11—44no—
481C2×C4×C11—44no—
482C2×C4×C11—48no—
483C2×C4×C11—44no—
484C2×C4×C11—84no—
485C2×C4×C11—84no—
486C2×C4×C11C22×D412yes—
487C2×C4×C11C22×D412yes—
488C2×C4×C11C22×D412yes—
489C2×C4×C11C22×D412yes—
490C2×C4×C11C22×D412yes—
491C2×C4×C11C2×#4112yes—
492C2×C4×C11C2×#4112yes—
493C2×C4×C11C2×#4112yes—
494C2×C4×C11C2×#4112yes—
495C2×C4×C11H(5,𝔽2)12yes—
496C2×C4×C112−1+412yes—
497C2×C4×C112−1+412yes—
498#539—216no—
499C2×C4⋊Q8C22×C1111yescharacteristic
500C2×#126C22×C1112yes—
501C2×#126C22×C1112yes—
502C2×#125C22×C1112yes—
503C2×#125C22×C1112yes—
504C2×#123C22×C1112yes—
505C2×#123C22×C1112yes—
506C2×#123C22×C1112yes—
507C2×#123C22×C1112yes—
508C2×#123C22×C1112yes—
509C2×C22⋊Q8C22×C1112yes—
510C2×C22⋊Q8C22×C1112yes—
511C2×C22⋊Q8C22×C1112yes—
512C2×#121C22×C1112yes—
513C2×#121C22×C1111yescharacteristic
514C2×#121C22×C1111yescharacteristic
515C2×C4×D4C22×C1112yes—
516C2×C4×D4C22×C1111yescharacteristic
517C2×C4×D4C22×C1111yescharacteristic
518C2×C4×D4C22×C1111yescharacteristic
519C2×C4×D4C22×C1111yescharacteristic
520C22×C4⋊C4C22×C1112yes—
521C22×C4⋊C4C22×C1111yescharacteristic
522C22×C4⋊C4C22×C1111yescharacteristic
523C22×C42C22×C1111yescharacteristic
524C22×C42C22×C1111yescharacteristic
525#400C22×C1112yes—
526#400C22×C1112yes—
527#399C22×C1112yes—
528#399C22×C1112yes—
529#398C22×C1112yes—
530#398C22×C1112yes—
531#398C22×C1112yes—
532#397C22×C1112yes—
533#397C22×C1112yes—
534#397C22×C1112yes—
535#396C22×C1112yes—
536#396C22×C1112yes—
537#395C22×C1112yes—
538#394C22×C1112yes—
539#394C22×C1112yes—
540#393C22×C1112yes—
541#391C22×C1112yes—
542#390C22×C1111yescharacteristic
543#390C22×C1111yescharacteristic
544#390C22×C1111yescharacteristic
545#390C22×C1111yescharacteristic
546#389C22×C1112yes—
547#389C22×C1112yes—
548#389C22×C1111yescharacteristic
549#389C22×C1111yescharacteristic
550#389C22×C1111yescharacteristic
551#389C22×C1111yescharacteristic
552#389C22×C1111yescharacteristic
553#389C22×C1112yes—
554#389C22×C1111yescharacteristic
555#389C22×C1111yescharacteristic
556#389C22×C1111yescharacteristic
557#389C22×C1112yes—
558#389C22×C1111yescharacteristic
559#389C22×C1111yescharacteristic
560#389C22×C1112yes—
561#388C22×C1112yes—
562#388C22×C1112yes—
563#388C22×C1112yes—
564#388C22×C1112yes—
565#388C22×C1112yes—
566#388C22×C1112yes—
567#387C22×C1112yes—
568#387C22×C1112yes—
569#386C22×C1112yes—
570#386C22×C1112yes—
571#386C22×C1112yes—
572#385C22×C1112yes—
573#385C22×C1112yes—
574#385C22×C1112yes—
575#384C22×C1111yescharacteristic
576#384C22×C1111yescharacteristic
577#384C22×C1111yescharacteristic
578#382C22×C1112yes—
579#381C22×C1112yes—
580#380C22×C1111yescharacteristic
581#380C22×C1111yescharacteristic
582#380C22×C1111yescharacteristic
583#380C22×C1112yes—
584#380C22×C1111yescharacteristic
585C4×C4⋊C4C22×C1111yescharacteristic
586C4×C4⋊C4C22×C1111yescharacteristic
587C4×C4⋊C4C22×C1111yescharacteristic
588C4×C4⋊C4C22×C1111yescharacteristic
589C4×C22⋊C4C22×C1111yescharacteristic
590C4×C22⋊C4C22×C1111yescharacteristic
591C4×C22⋊C4C22×C1111yescharacteristic
592C4×C22⋊C4C22×C1111yescharacteristic
593C4×C22⋊C4C22×C1111yescharacteristic
594C4×C22⋊C4C22×C1111yescharacteristic
595C4×C22⋊C4C22×C1112yes—
596C2×#95C22×C1112yes—
597C43C22×C1111yescharacteristic
598C22×C11—22no—
599C22×C11—22no—
600C22×C11—22no—
601C22×C11—22no—
602C22×C11—22no—
603C22×C11—22no—
604C22×C11—22no—
605C22×C11—22no—
606C22×C11—22no—
607C22×C11—41no—
608C22×C11—41no—
609C22×C11—41no—
610C22×C11—41no—
611C22×C11—42no—
612C22×C11—42no—
613C22×C11—42no—
614C22×C11—42no—
615C22×C11—42no—
616C22×C11—42no—
617C22×C11—42no—
618C22×C11#53214yes—
619C22×C11C23×D411yescharacteristic
620C22×C11C22×#4111yescharacteristic
621C22×C11C22×#4111yescharacteristic
622C22×C11C2×H(5,𝔽2)11yescharacteristic
623C22×C11C2×2−1+411yescharacteristic
624C22×C11C2×2−1+411yescharacteristic
625C22×C11#58511yescharacteristic
626C4×C11—22no—
627C4×C11—22no—
628C4×C11—22no—
629C4×C11—22no—
630C4×C11—22no—
631C4×C11—22no—
632C4×C11—22no—
633C4×C11—22no—
634C4×C11—22no—
635C4×C11—42no—
636C4×C11—42no—
637C4×C11—42no—
638C4×C11—41no—
639C4×C11—41no—
640C4×C11—42no—
641C4×C11—42no—
642C4×C11—42no—
643C4×C11—42no—
644C4×C11—41no—
645C4×C11#53914yescomplemented
646C22×Q8C23×C1112yes—
647C22×D4C23×C1112yes—
648C22×D4C23×C1111yescharacteristic
649C22×D4C23×C1111yescharacteristic
650C22×D4C23×C1112yes—
651C23×C4C23×C1112yes—
652C23×C4C23×C1111yescharacteristic
653C23×C4C23×C1111yescharacteristic
654C23×C4C23×C1111yescharacteristic
655C23×C4C23×C1111yescharacteristic
656C23×C4C23×C1112yes—
657C23×C4C23×C1112yes—
658C23×C4C23×C1111yescharacteristic
659C23×C4C23×C1111yescharacteristic
660C4⋊Q8—42no—
661#126—28no—
662#126—28no—
663#125—28no—
664#125—28no—
665#123—28no—
666#123—28no—
667#123—28no—
668#123—28no—
669#123—28no—
670C22⋊Q8—28no—
671C22⋊Q8—28no—
672C22⋊Q8—28no—
673#121—28no—
674#121—24no—
675#121—42no—
676C4×D4—28no—
677C4×D4—24no—
678C4×D4—24no—
679C4×D4—42no—
680C4×D4D4×C1118yescomplemented
681C2×C4⋊C4—28no—
682C2×C4⋊C4—24no—
683C2×C4⋊C4—42no—
684C2×C4⋊C4C23×C1111yescharacteristic
685C2×C4⋊C4C23×C1112yes—
686C2×C4⋊C4C23×C1112yes—
687C2×C4⋊C4C23×C1112yes—
688C2×C4⋊C4C23×C1112yes—
689C2×C4⋊C4C23×C1111yescharacteristic
690C2×C4⋊C4C23×C1111yescharacteristic
691C2×C4⋊C4C23×C1111yescharacteristic
692C2×C4⋊C4C23×C1112yes—
693C2×C4⋊C4C23×C1112yes—
694C2×C4⋊C4C23×C1111yescharacteristic
695C2×C4⋊C4C23×C1111yescharacteristic
696C2×C4⋊C4C23×C1111yescharacteristic
697C2×C4⋊C4C23×C1112yes—
698C2×C4⋊C4C23×C1111yescharacteristic
699C2×C4⋊C4C23×C1112yes—
700C2×C4⋊C4C23×C1112yes—
701C2×C4⋊C4C23×C1112yes—
702C2×C4⋊C4C23×C1112yes—
703C2×C4⋊C4C23×C1112yes—
704C2×C4⋊C4C23×C1112yes—
705C2×C4⋊C4C23×C1112yes—
706C2×C4⋊C4C23×C1112yes—
707C2×C4⋊C4C23×C1112yes—
708C2×C4⋊C4C23×C1111yescharacteristic
709C2×C4⋊C4C23×C1112yes—
710C2×C4⋊C4C23×C1112yes—
711C2×C4⋊C4C23×C1112yes—
712C2×C4⋊C4C23×C1111yescharacteristic
713C2×C22⋊C4C23×C1112yes—
714C2×C22⋊C4C23×C1112yes—
715C2×C22⋊C4C23×C1111yescharacteristic
716C2×C22⋊C4C23×C1111yescharacteristic
717C2×C22⋊C4C23×C1111yescharacteristic
718C2×C22⋊C4C23×C1112yes—
719C2×C22⋊C4C23×C1112yes—
720C2×C22⋊C4C23×C1112yes—
721C2×C22⋊C4C23×C1112yes—
722C2×C22⋊C4C23×C1112yes—
723C2×C22⋊C4C23×C1112yes—
724C2×C22⋊C4C23×C1112yes—
725C2×C22⋊C4C23×C1112yes—
726C2×C22⋊C4C23×C1112yes—
727C2×C22⋊C4C23×C1112yes—
728C2×C22⋊C4C23×C1112yes—
729C2×C22⋊C4C23×C1112yes—
730C2×C22⋊C4C23×C1112yes—
731C2×C22⋊C4C23×C1111yescharacteristic
732C2×C22⋊C4C23×C1111yescharacteristic
733C2×C22⋊C4C23×C1111yescharacteristic
734C2×C42—42no—
735C2×C42—42no—
736C2×C42C23×C1112yes—
737C2×C42C23×C1111yescharacteristic
738C2×C42C23×C1111yescharacteristic
739C2×C42C23×C1111yescharacteristic
740C2×C42C23×C1111yescharacteristic
741C2×C42C23×C1111yescharacteristic
742C2×C42C23×C1111yescharacteristic
743C2×C42C23×C1111yescharacteristic
744C2×C42C23×C1111yescharacteristic
745C2×C42C23×C1111yescharacteristic
746C2×C42C23×C1111yescharacteristic
747C2×C42C23×C1111yescharacteristic
748C2×C42C23×C1111yescharacteristic
749C2×C42C23×C1111yescharacteristic
750#95C23×C1112yes—
751#95C23×C1112yes—
752#95C23×C1112yes—
753#95C23×C1112yes—
754#95C23×C1111yescharacteristic
755#95C23×C1111yescharacteristic
756#95C23×C1111yescharacteristic
757#95C23×C1111yescharacteristic
758#95C23×C1111yescharacteristic
759#95C23×C1111yescharacteristic
760#95C23×C1112yes—
761#95C23×C1112yes—
762#95C23×C1112yes—
763#95C23×C1112yes—
764#95C23×C1112yes—
765#95C23×C1112yes—
766#95C23×C1112yes—
767#95C23×C1112yes—
768#95C23×C1112yes—
769#95C23×C1112yes—
770#95C23×C1112yes—
771C2×C11—24no—
772C2×C11—42no—
773C2×C11—82no—
774C2×C11C2×#53211yescharacteristic
775C2×C11C2×#53911yescharacteristic
776C2×C11#346111yescharacteristic
777C2×C11#349611yescharacteristic
778C2×C11#349911yescharacteristic
779C2×C11#351511yescharacteristic
780C2×C11#352011yescharacteristic
781C24C24×C1112yes—
782C24C24×C1111yescharacteristic
783C24C24×C1111yescharacteristic
784C2×Q8—24no—
785C2×Q8—42no—
786C2×Q8—42no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—24no—
792C2×D4—24no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4C2×D4×C1114yes—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—22no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—24no—
813C22×C4—41no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—41no—
817C22×C4—41no—
818C22×C4—41no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4C2×D4×C1114yes—
824C22×C4C2×D4×C1114yes—
825C22×C4C11×#4114yes—
826C22×C4C24×C1111yescharacteristic
827C22×C4C24×C1111yescharacteristic
828C22×C4C24×C1111yescharacteristic
829C22×C4C24×C1112yes—
830C22×C4C24×C1112yes—
831C22×C4C24×C1112yes—
832C22×C4C24×C1112yes—
833C22×C4C24×C1112yes—
834C22×C4C24×C1112yes—
835C22×C4C24×C1112yes—
836C22×C4C24×C1111yescharacteristic
837C22×C4C24×C1111yescharacteristic
838C22×C4C24×C1111yescharacteristic
839C22×C4C24×C1111yescharacteristic
840C22×C4C24×C1111yescharacteristic
841C22×C4C24×C1111yescharacteristic
842C22×C4C24×C1111yescharacteristic
843C22×C4C24×C1111yescharacteristic
844C22×C4C24×C1111yescharacteristic
845C22×C4C24×C1111yescharacteristic
846C4⋊C4—24no—
847C4⋊C4—24no—
848C4⋊C4—24no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—24no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—22no—
871C4⋊C4—42no—
872C4⋊C4—42no—
873C4⋊C4—42no—
874C4⋊C4C2×D4×C1114yes—
875C22⋊C4—24no—
876C22⋊C4—24no—
877C22⋊C4—24no—
878C22⋊C4—24no—
879C22⋊C4—22no—
880C22⋊C4—24no—
881C22⋊C4—24no—
882C22⋊C4—24no—
883C22⋊C4—24no—
884C22⋊C4—22no—
885C22⋊C4—22no—
886C22⋊C4—24no—
887C22⋊C4—24no—
888C22⋊C4—24no—
889C22⋊C4—24no—
890C22⋊C4—42no—
891C22⋊C4—42no—
892C22⋊C4—42no—
893C22⋊C4C2×D4×C1114yes—
894C22⋊C4C2×D4×C1114yes—
895C22⋊C4C11×#4114yes—
896C42—24no—
897C42—22no—
898C42—22no—
899C42—22no—
900C42—22no—
901C42—22no—
902C42—22no—
903C42—22no—
904C42—41no—
905C42—41no—
906C42—41no—
907C42—41no—
908C42—41no—
909C42C2×D4×C1114yes—
910C11#3500811yescharacteristic, direct product factor, Sylow
911C23—21no—
912C23—21no—
913C23—21no—
914C23—21no—
915C23—21no—
916C23—21no—
917C23—21no—
918C23—21no—
919C23—21no—
920C23—21no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23C22×D4×C1112yes—
929C23C22×D4×C1112yes—
930C23C2×C11×#4112yes—
931C23C2×C11×#4112yes—
932C23C25×C1111yescharacteristic
933Q8—84no—
934D4—28no—
935D4—48no—
936D4—44no—
937D4—84no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—28no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—21no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—44no—
988C2×C4—44no—
989C2×C4—44no—
990C2×C4—44no—
991C2×C4—48no—
992C2×C4—44no—
993C2×C4—84no—
994C2×C4—84no—
995C2×C4C22×D4×C1112yes—
996C2×C4C22×D4×C1112yes—
997C2×C4C22×D4×C1112yes—
998C2×C4C22×D4×C1112yes—
999C2×C4C22×D4×C1112yes—
1000C2×C4C2×C11×#4112yes—
1001C2×C4C2×C11×#4112yes—
1002C2×C4C2×C11×#4112yes—
1003C2×C4C2×C11×#4112yes—
1004C2×C4C11×H(5,𝔽2)12yes—
1005C2×C4C11×2−1+412yes—
1006C2×C4C11×2−1+412yes—
1007C22—22no—
1008C22—22no—
1009C22—22no—
1010C22—22no—
1011C22—22no—
1012C22—22no—
1013C22—22no—
1014C22—22no—
1015C22—22no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—42no—
1021C22—42no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22C11×#53214yes—
1028C22C23×D4×C1111yescharacteristic
1029C22C22×C11×#4111yescharacteristic
1030C22C22×C11×#4111yescharacteristic
1031C22C2×C11×H(5,𝔽2)11yescharacteristic
1032C22C2×C11×2−1+411yescharacteristic
1033C22C2×C11×2−1+411yescharacteristic
1034C22C11×#58511yescharacteristic
1035C4—22no—
1036C4—22no—
1037C4—22no—
1038C4—22no—
1039C4—22no—
1040C4—22no—
1041C4—22no—
1042C4—22no—
1043C4—22no—
1044C4—42no—
1045C4—42no—
1046C4—42no—
1047C4—41no—
1048C4—41no—
1049C4—42no—
1050C4—42no—
1051C4—42no—
1052C4—42no—
1053C4—41no—
1054C4C11×#53914yescomplemented
1055C2—24no—
1056C2—42no—
1057C2—82no—
1058C2C2×C11×#53211yescharacteristic
1059C2C2×C11×#53911yescharacteristic
1060C2C11×#346111yescharacteristic
1061C2C11×#349611yescharacteristic
1062C2C11×#349911yescharacteristic
1063C2C11×#351511yescharacteristic
1064C2C11×#352011yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutator, Frattini, cosocleC23C25×C11
prime radicalC11×#2416C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C11×#539C2semidirect
2. C11×#2860C2semidirect
3. C11×#2859C2semidirect
4. C11×#2857C2semidirect
5. C11×#2854C2semidirect
6. C11×#2664C2semidirect
7. C11×#2663C2semidirect
8. C11×#2556C2semidirect
9. C11×#2553C2semidirect
10. C11×#2506C2semidirect
11. C11×#2501C2semidirect
12. C11×#2496C2semidirect
13. C11×#2488C2semidirect
14. C11×#2486C2semidirect
15. C11×#2452C2semidirect
16. C11×#2440C2semidirect
17. C11×#2425C2semidirect
18. C11×#2422C2semidirect
20. C11×#2322C2semidirect
21. C4×C11×#121C2semidirect
22. C2×C11×#389C2semidirect
23. C42×D4×C11C2semidirect
158. C4×D4×C11D4semidirect
249. #35008C11direct (N × H)
379. C2×#539C2×C11semidirect
380. #2860C2×C11semidirect
381. #2859C2×C11semidirect
382. #2857C2×C11semidirect
383. #2854C2×C11semidirect
384. #2664C2×C11semidirect
385. #2663C2×C11semidirect
386. #2556C2×C11semidirect
387. #2553C2×C11semidirect
388. #2506C2×C11semidirect
389. #2501C2×C11semidirect
390. #2496C2×C11semidirect
391. #2488C2×C11semidirect
392. #2486C2×C11semidirect
393. #2452C2×C11semidirect
394. #2440C2×C11semidirect
395. #2425C2×C11semidirect
396. #2422C2×C11semidirect
398. #2322C2×C11semidirect
399. C4×#121C2×C11semidirect
400. C2×#389C2×C11semidirect
401. C42×D4C2×C11semidirect
645. C4×C11#539semidirect
680. C4×D4D4×C11semidirect
910. C11#35008direct (N × H)
1054. C4C11×#539semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C11×#5392
C11×#28602
C11×#28592
C11×#28572
C11×#28542
C11×#26642
C11×#26632
C11×#25562
C11×#25532
C11×#25062
C11×#25012
C11×#24962
C11×#24882
C11×#24862
C11×#24522
C11×#24402
C11×#24252
C11×#24222
C11×#24162
C11×#23222
C4×C11×#1212
C2×C11×#3892
C42×D4×C112
#3500811